Can someone explain to me in simple terms what a Linear regression model’s residual term is?

You have some pair values of X and Y. You are trying to find if there is a linear relationship existing between X and Y in order to predict values of Y for a given value of X. You plot these pairs on a graph and estimate a regression line thru these pairs. Some of the points will lie on the line, while many may not. Next, your aim is to find the deviation of Y values from its mean Y bar. For a point that actually lies on the estimated line, this difference Y - Y bar = Y hat - Y bar. This is called the explained error, which has been explained by the estimated line. But for a point that does not lie on the line, difference Y - Y bar = (Y - Y hat) + (Y hat - Y bar). The component (Y - Y hat), which is not explained by the estimated line is the residual term. Read the text (CFAI/Schswser) with reference to the graph there and it should not be difficult to comprehend.

Wow, that was really too much… Take your model, stick an X value in it, calculate the Y value, and compare it to the actual Y value. The difference is the residual (error). That’s it.